Is it possible to change the emission rate of particles over time?
In short, there's no ready solution. Lukas Tönne was responsible for a feature known as "Paged Buffers for Particles" but at some point he stopped working on it and the feature never made it to trunk. Here's a timeline of what happened:


March 11 2011: This video shows that variable particle emission was working.
March 17 2011: Paged Buffers for Particles research was published on Blender's developer blog.
July 22 2011: A crowd-funding campaign launched through Lukas's blog.
Dec 6 2011: Lukas spoke about his progress at the 2011 Blender Conference.
May 4 2012: Last blog post on the subject.
August 4 2013: Lukas was hired to do general bug fixing with the Blender Foundation. His work would be "especially for nodes and [the] compositor. When time allows, he then can also pick up work on new particle system."
August 26 2013: In episode 26 of the Blender Podcast, Lukas stated "I started working on the particles, but there are a few basic issues that need to be fixed on a more general level before I can go into the details of node-ifying particles and things like that."
2014–Present: His tweets about node development continue to mention relevant subject matter including duplis which will eventually feed into particle nodes.
Nov 1, 2015: B2.8 project developer kickoff meeting notes mentions that "The particle system and constraints may need a complete overhaul."